Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 1 | // Ceres Solver - A fast non-linear least squares minimizer |
| 2 | // Copyright 2012 Google Inc. All rights reserved. |
| 3 | // http://code.google.com/p/ceres-solver/ |
| 4 | // |
| 5 | // Redistribution and use in source and binary forms, with or without |
| 6 | // modification, are permitted provided that the following conditions are met: |
| 7 | // |
| 8 | // * Redistributions of source code must retain the above copyright notice, |
| 9 | // this list of conditions and the following disclaimer. |
| 10 | // * Redistributions in binary form must reproduce the above copyright notice, |
| 11 | // this list of conditions and the following disclaimer in the documentation |
| 12 | // and/or other materials provided with the distribution. |
| 13 | // * Neither the name of Google Inc. nor the names of its contributors may be |
| 14 | // used to endorse or promote products derived from this software without |
| 15 | // specific prior written permission. |
| 16 | // |
| 17 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| 18 | // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 19 | // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 20 | // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| 21 | // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| 22 | // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| 23 | // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| 24 | // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| 25 | // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 26 | // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| 27 | // POSSIBILITY OF SUCH DAMAGE. |
| 28 | // |
| 29 | // Author: sameeragarwal@google.com (Sameer Agarwal) |
| 30 | |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 31 | #include <iomanip> |
| 32 | #include <iostream> // NOLINT |
| 33 | |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 34 | #include "ceres/line_search.h" |
| 35 | |
| 36 | #include "ceres/fpclassify.h" |
| 37 | #include "ceres/evaluator.h" |
| 38 | #include "ceres/internal/eigen.h" |
| 39 | #include "ceres/polynomial.h" |
| 40 | #include "ceres/stringprintf.h" |
| 41 | #include "glog/logging.h" |
| 42 | |
| 43 | namespace ceres { |
| 44 | namespace internal { |
| 45 | namespace { |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 46 | // Precision used for floating point values in error message output. |
| 47 | const int kErrorMessageNumericPrecision = 8; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 48 | |
| 49 | FunctionSample ValueSample(const double x, const double value) { |
| 50 | FunctionSample sample; |
| 51 | sample.x = x; |
| 52 | sample.value = value; |
| 53 | sample.value_is_valid = true; |
| 54 | return sample; |
| 55 | }; |
| 56 | |
| 57 | FunctionSample ValueAndGradientSample(const double x, |
| 58 | const double value, |
| 59 | const double gradient) { |
| 60 | FunctionSample sample; |
| 61 | sample.x = x; |
| 62 | sample.value = value; |
| 63 | sample.gradient = gradient; |
| 64 | sample.value_is_valid = true; |
| 65 | sample.gradient_is_valid = true; |
| 66 | return sample; |
| 67 | }; |
| 68 | |
| 69 | } // namespace |
| 70 | |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 71 | |
| 72 | std::ostream& operator<<(std::ostream &os, const FunctionSample& sample); |
| 73 | |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 74 | // Convenience stream operator for pushing FunctionSamples into log messages. |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 75 | std::ostream& operator<<(std::ostream &os, const FunctionSample& sample) { |
| 76 | os << sample.ToDebugString(); |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 77 | return os; |
| 78 | } |
| 79 | |
| 80 | LineSearch::LineSearch(const LineSearch::Options& options) |
| 81 | : options_(options) {} |
| 82 | |
| 83 | LineSearch* LineSearch::Create(const LineSearchType line_search_type, |
| 84 | const LineSearch::Options& options, |
| 85 | string* error) { |
| 86 | LineSearch* line_search = NULL; |
| 87 | switch (line_search_type) { |
| 88 | case ceres::ARMIJO: |
| 89 | line_search = new ArmijoLineSearch(options); |
| 90 | break; |
| 91 | case ceres::WOLFE: |
| 92 | line_search = new WolfeLineSearch(options); |
| 93 | break; |
| 94 | default: |
| 95 | *error = string("Invalid line search algorithm type: ") + |
| 96 | LineSearchTypeToString(line_search_type) + |
| 97 | string(", unable to create line search."); |
| 98 | return NULL; |
| 99 | } |
| 100 | return line_search; |
| 101 | } |
| 102 | |
| 103 | LineSearchFunction::LineSearchFunction(Evaluator* evaluator) |
| 104 | : evaluator_(evaluator), |
| 105 | position_(evaluator->NumParameters()), |
| 106 | direction_(evaluator->NumEffectiveParameters()), |
| 107 | evaluation_point_(evaluator->NumParameters()), |
| 108 | scaled_direction_(evaluator->NumEffectiveParameters()), |
| 109 | gradient_(evaluator->NumEffectiveParameters()) { |
| 110 | } |
| 111 | |
| 112 | void LineSearchFunction::Init(const Vector& position, |
| 113 | const Vector& direction) { |
| 114 | position_ = position; |
| 115 | direction_ = direction; |
| 116 | } |
| 117 | |
Scott Ettinger | 399f7d0 | 2013-09-09 12:54:43 -0700 | [diff] [blame] | 118 | bool LineSearchFunction::Evaluate(double x, double* f, double* g) { |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 119 | scaled_direction_ = x * direction_; |
| 120 | if (!evaluator_->Plus(position_.data(), |
| 121 | scaled_direction_.data(), |
| 122 | evaluation_point_.data())) { |
| 123 | return false; |
| 124 | } |
| 125 | |
| 126 | if (g == NULL) { |
| 127 | return (evaluator_->Evaluate(evaluation_point_.data(), |
| 128 | f, NULL, NULL, NULL) && |
| 129 | IsFinite(*f)); |
| 130 | } |
| 131 | |
| 132 | if (!evaluator_->Evaluate(evaluation_point_.data(), |
| 133 | f, |
| 134 | NULL, |
| 135 | gradient_.data(), NULL)) { |
| 136 | return false; |
| 137 | } |
| 138 | |
| 139 | *g = direction_.dot(gradient_); |
| 140 | return IsFinite(*f) && IsFinite(*g); |
| 141 | } |
| 142 | |
| 143 | double LineSearchFunction::DirectionInfinityNorm() const { |
| 144 | return direction_.lpNorm<Eigen::Infinity>(); |
| 145 | } |
| 146 | |
| 147 | // Returns step_size \in [min_step_size, max_step_size] which minimizes the |
| 148 | // polynomial of degree defined by interpolation_type which interpolates all |
| 149 | // of the provided samples with valid values. |
| 150 | double LineSearch::InterpolatingPolynomialMinimizingStepSize( |
| 151 | const LineSearchInterpolationType& interpolation_type, |
| 152 | const FunctionSample& lowerbound, |
| 153 | const FunctionSample& previous, |
| 154 | const FunctionSample& current, |
| 155 | const double min_step_size, |
| 156 | const double max_step_size) const { |
| 157 | if (!current.value_is_valid || |
| 158 | (interpolation_type == BISECTION && |
| 159 | max_step_size <= current.x)) { |
| 160 | // Either: sample is invalid; or we are using BISECTION and contracting |
| 161 | // the step size. |
| 162 | return min(max(current.x * 0.5, min_step_size), max_step_size); |
| 163 | } else if (interpolation_type == BISECTION) { |
| 164 | CHECK_GT(max_step_size, current.x); |
| 165 | // We are expanding the search (during a Wolfe bracketing phase) using |
| 166 | // BISECTION interpolation. Using BISECTION when trying to expand is |
| 167 | // strictly speaking an oxymoron, but we define this to mean always taking |
| 168 | // the maximum step size so that the Armijo & Wolfe implementations are |
| 169 | // agnostic to the interpolation type. |
| 170 | return max_step_size; |
| 171 | } |
| 172 | // Only check if lower-bound is valid here, where it is required |
| 173 | // to avoid replicating current.value_is_valid == false |
| 174 | // behaviour in WolfeLineSearch. |
| 175 | CHECK(lowerbound.value_is_valid) |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 176 | << std::scientific << std::setprecision(kErrorMessageNumericPrecision) |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 177 | << "Ceres bug: lower-bound sample for interpolation is invalid, " |
| 178 | << "please contact the developers!, interpolation_type: " |
| 179 | << LineSearchInterpolationTypeToString(interpolation_type) |
| 180 | << ", lowerbound: " << lowerbound << ", previous: " << previous |
| 181 | << ", current: " << current; |
| 182 | |
| 183 | // Select step size by interpolating the function and gradient values |
| 184 | // and minimizing the corresponding polynomial. |
| 185 | vector<FunctionSample> samples; |
| 186 | samples.push_back(lowerbound); |
| 187 | |
| 188 | if (interpolation_type == QUADRATIC) { |
| 189 | // Two point interpolation using function values and the |
| 190 | // gradient at the lower bound. |
| 191 | samples.push_back(ValueSample(current.x, current.value)); |
| 192 | |
| 193 | if (previous.value_is_valid) { |
| 194 | // Three point interpolation, using function values and the |
| 195 | // gradient at the lower bound. |
| 196 | samples.push_back(ValueSample(previous.x, previous.value)); |
| 197 | } |
| 198 | } else if (interpolation_type == CUBIC) { |
| 199 | // Two point interpolation using the function values and the gradients. |
| 200 | samples.push_back(current); |
| 201 | |
| 202 | if (previous.value_is_valid) { |
| 203 | // Three point interpolation using the function values and |
| 204 | // the gradients. |
| 205 | samples.push_back(previous); |
| 206 | } |
| 207 | } else { |
| 208 | LOG(FATAL) << "Ceres bug: No handler for interpolation_type: " |
| 209 | << LineSearchInterpolationTypeToString(interpolation_type) |
| 210 | << ", please contact the developers!"; |
| 211 | } |
| 212 | |
| 213 | double step_size = 0.0, unused_min_value = 0.0; |
| 214 | MinimizeInterpolatingPolynomial(samples, min_step_size, max_step_size, |
| 215 | &step_size, &unused_min_value); |
| 216 | return step_size; |
| 217 | } |
| 218 | |
| 219 | ArmijoLineSearch::ArmijoLineSearch(const LineSearch::Options& options) |
| 220 | : LineSearch(options) {} |
| 221 | |
| 222 | void ArmijoLineSearch::Search(const double step_size_estimate, |
| 223 | const double initial_cost, |
| 224 | const double initial_gradient, |
| 225 | Summary* summary) { |
| 226 | *CHECK_NOTNULL(summary) = LineSearch::Summary(); |
| 227 | CHECK_GE(step_size_estimate, 0.0); |
| 228 | CHECK_GT(options().sufficient_decrease, 0.0); |
| 229 | CHECK_LT(options().sufficient_decrease, 1.0); |
| 230 | CHECK_GT(options().max_num_iterations, 0); |
| 231 | Function* function = options().function; |
| 232 | |
| 233 | // Note initial_cost & initial_gradient are evaluated at step_size = 0, |
| 234 | // not step_size_estimate, which is our starting guess. |
| 235 | const FunctionSample initial_position = |
| 236 | ValueAndGradientSample(0.0, initial_cost, initial_gradient); |
| 237 | |
| 238 | FunctionSample previous = ValueAndGradientSample(0.0, 0.0, 0.0); |
| 239 | previous.value_is_valid = false; |
| 240 | |
| 241 | FunctionSample current = ValueAndGradientSample(step_size_estimate, 0.0, 0.0); |
| 242 | current.value_is_valid = false; |
| 243 | |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 244 | // As the Armijo line search algorithm always uses the initial point, for |
| 245 | // which both the function value and derivative are known, when fitting a |
| 246 | // minimizing polynomial, we can fit up to a quadratic without requiring the |
| 247 | // gradient at the current query point. |
| 248 | const bool interpolation_uses_gradient_at_current_sample = |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 249 | options().interpolation_type == CUBIC; |
| 250 | const double descent_direction_max_norm = |
| 251 | static_cast<const LineSearchFunction*>(function)->DirectionInfinityNorm(); |
| 252 | |
| 253 | ++summary->num_function_evaluations; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 254 | if (interpolation_uses_gradient_at_current_sample) { |
| 255 | ++summary->num_gradient_evaluations; |
| 256 | } |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 257 | current.value_is_valid = |
| 258 | function->Evaluate(current.x, |
| 259 | ¤t.value, |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 260 | interpolation_uses_gradient_at_current_sample |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 261 | ? ¤t.gradient : NULL); |
| 262 | current.gradient_is_valid = |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 263 | interpolation_uses_gradient_at_current_sample && current.value_is_valid; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 264 | while (!current.value_is_valid || |
| 265 | current.value > (initial_cost |
| 266 | + options().sufficient_decrease |
| 267 | * initial_gradient |
| 268 | * current.x)) { |
| 269 | // If current.value_is_valid is false, we treat it as if the cost at that |
| 270 | // point is not large enough to satisfy the sufficient decrease condition. |
| 271 | ++summary->num_iterations; |
| 272 | if (summary->num_iterations >= options().max_num_iterations) { |
| 273 | summary->error = |
| 274 | StringPrintf("Line search failed: Armijo failed to find a point " |
| 275 | "satisfying the sufficient decrease condition within " |
| 276 | "specified max_num_iterations: %d.", |
| 277 | options().max_num_iterations); |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 278 | LOG_IF(WARNING, !options().is_silent) << summary->error; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 279 | return; |
| 280 | } |
| 281 | |
| 282 | const double step_size = |
| 283 | this->InterpolatingPolynomialMinimizingStepSize( |
| 284 | options().interpolation_type, |
| 285 | initial_position, |
| 286 | previous, |
| 287 | current, |
| 288 | (options().max_step_contraction * current.x), |
| 289 | (options().min_step_contraction * current.x)); |
| 290 | |
| 291 | if (step_size * descent_direction_max_norm < options().min_step_size) { |
| 292 | summary->error = |
| 293 | StringPrintf("Line search failed: step_size too small: %.5e " |
| 294 | "with descent_direction_max_norm: %.5e.", step_size, |
| 295 | descent_direction_max_norm); |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 296 | LOG_IF(WARNING, !options().is_silent) << summary->error; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 297 | return; |
| 298 | } |
| 299 | |
| 300 | previous = current; |
| 301 | current.x = step_size; |
| 302 | |
| 303 | ++summary->num_function_evaluations; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 304 | if (interpolation_uses_gradient_at_current_sample) { |
| 305 | ++summary->num_gradient_evaluations; |
| 306 | } |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 307 | current.value_is_valid = |
| 308 | function->Evaluate(current.x, |
| 309 | ¤t.value, |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 310 | interpolation_uses_gradient_at_current_sample |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 311 | ? ¤t.gradient : NULL); |
| 312 | current.gradient_is_valid = |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 313 | interpolation_uses_gradient_at_current_sample && current.value_is_valid; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 314 | } |
| 315 | |
| 316 | summary->optimal_step_size = current.x; |
| 317 | summary->success = true; |
| 318 | } |
| 319 | |
| 320 | WolfeLineSearch::WolfeLineSearch(const LineSearch::Options& options) |
| 321 | : LineSearch(options) {} |
| 322 | |
| 323 | void WolfeLineSearch::Search(const double step_size_estimate, |
| 324 | const double initial_cost, |
| 325 | const double initial_gradient, |
| 326 | Summary* summary) { |
| 327 | *CHECK_NOTNULL(summary) = LineSearch::Summary(); |
| 328 | // All parameters should have been validated by the Solver, but as |
| 329 | // invalid values would produce crazy nonsense, hard check them here. |
| 330 | CHECK_GE(step_size_estimate, 0.0); |
| 331 | CHECK_GT(options().sufficient_decrease, 0.0); |
| 332 | CHECK_GT(options().sufficient_curvature_decrease, |
| 333 | options().sufficient_decrease); |
| 334 | CHECK_LT(options().sufficient_curvature_decrease, 1.0); |
| 335 | CHECK_GT(options().max_step_expansion, 1.0); |
| 336 | |
| 337 | // Note initial_cost & initial_gradient are evaluated at step_size = 0, |
| 338 | // not step_size_estimate, which is our starting guess. |
| 339 | const FunctionSample initial_position = |
| 340 | ValueAndGradientSample(0.0, initial_cost, initial_gradient); |
| 341 | |
| 342 | bool do_zoom_search = false; |
| 343 | // Important: The high/low in bracket_high & bracket_low refer to their |
| 344 | // _function_ values, not their step sizes i.e. it is _not_ required that |
| 345 | // bracket_low.x < bracket_high.x. |
| 346 | FunctionSample solution, bracket_low, bracket_high; |
| 347 | |
| 348 | // Wolfe bracketing phase: Increases step_size until either it finds a point |
| 349 | // that satisfies the (strong) Wolfe conditions, or an interval that brackets |
| 350 | // step sizes which satisfy the conditions. From Nocedal & Wright [1] p61 the |
| 351 | // interval: (step_size_{k-1}, step_size_{k}) contains step lengths satisfying |
| 352 | // the strong Wolfe conditions if one of the following conditions are met: |
| 353 | // |
| 354 | // 1. step_size_{k} violates the sufficient decrease (Armijo) condition. |
| 355 | // 2. f(step_size_{k}) >= f(step_size_{k-1}). |
| 356 | // 3. f'(step_size_{k}) >= 0. |
| 357 | // |
| 358 | // Caveat: If f(step_size_{k}) is invalid, then step_size is reduced, ignoring |
| 359 | // this special case, step_size monotonically increases during bracketing. |
| 360 | if (!this->BracketingPhase(initial_position, |
| 361 | step_size_estimate, |
| 362 | &bracket_low, |
| 363 | &bracket_high, |
| 364 | &do_zoom_search, |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 365 | summary)) { |
| 366 | // Failed to find either a valid point, a valid bracket satisfying the Wolfe |
| 367 | // conditions, or even a step size > minimum tolerance satisfying the Armijo |
| 368 | // condition. |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 369 | return; |
| 370 | } |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 371 | |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 372 | if (!do_zoom_search) { |
| 373 | // Either: Bracketing phase already found a point satisfying the strong |
| 374 | // Wolfe conditions, thus no Zoom required. |
| 375 | // |
| 376 | // Or: Bracketing failed to find a valid bracket or a point satisfying the |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 377 | // strong Wolfe conditions within max_num_iterations, or whilst searching |
| 378 | // shrank the bracket width until it was below our minimum tolerance. |
| 379 | // As these are 'artificial' constraints, and we would otherwise fail to |
| 380 | // produce a valid point when ArmijoLineSearch would succeed, we return the |
| 381 | // point with the lowest cost found thus far which satsifies the Armijo |
| 382 | // condition (but not the Wolfe conditions). |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 383 | summary->optimal_step_size = bracket_low.x; |
| 384 | summary->success = true; |
| 385 | return; |
| 386 | } |
| 387 | |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 388 | VLOG(3) << std::scientific << std::setprecision(kErrorMessageNumericPrecision) |
| 389 | << "Starting line search zoom phase with bracket_low: " |
| 390 | << bracket_low << ", bracket_high: " << bracket_high |
| 391 | << ", bracket width: " << fabs(bracket_low.x - bracket_high.x) |
| 392 | << ", bracket abs delta cost: " |
| 393 | << fabs(bracket_low.value - bracket_high.value); |
| 394 | |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 395 | // Wolfe Zoom phase: Called when the Bracketing phase finds an interval of |
| 396 | // non-zero, finite width that should bracket step sizes which satisfy the |
| 397 | // (strong) Wolfe conditions (before finding a step size that satisfies the |
| 398 | // conditions). Zoom successively decreases the size of the interval until a |
| 399 | // step size which satisfies the Wolfe conditions is found. The interval is |
| 400 | // defined by bracket_low & bracket_high, which satisfy: |
| 401 | // |
| 402 | // 1. The interval bounded by step sizes: bracket_low.x & bracket_high.x |
| 403 | // contains step sizes that satsify the strong Wolfe conditions. |
| 404 | // 2. bracket_low.x is of all the step sizes evaluated *which satisifed the |
| 405 | // Armijo sufficient decrease condition*, the one which generated the |
| 406 | // smallest function value, i.e. bracket_low.value < |
| 407 | // f(all other steps satisfying Armijo). |
| 408 | // - Note that this does _not_ (necessarily) mean that initially |
| 409 | // bracket_low.value < bracket_high.value (although this is typical) |
| 410 | // e.g. when bracket_low = initial_position, and bracket_high is the |
| 411 | // first sample, and which does not satisfy the Armijo condition, |
| 412 | // but still has bracket_high.value < initial_position.value. |
| 413 | // 3. bracket_high is chosen after bracket_low, s.t. |
| 414 | // bracket_low.gradient * (bracket_high.x - bracket_low.x) < 0. |
| 415 | if (!this->ZoomPhase(initial_position, |
| 416 | bracket_low, |
| 417 | bracket_high, |
| 418 | &solution, |
| 419 | summary) && !solution.value_is_valid) { |
| 420 | // Failed to find a valid point (given the specified decrease parameters) |
| 421 | // within the specified bracket. |
| 422 | return; |
| 423 | } |
| 424 | // Ensure that if we ran out of iterations whilst zooming the bracket, or |
| 425 | // shrank the bracket width to < tolerance and failed to find a point which |
| 426 | // satisfies the strong Wolfe curvature condition, that we return the point |
| 427 | // amongst those found thus far, which minimizes f() and satisfies the Armijo |
| 428 | // condition. |
| 429 | solution = |
| 430 | solution.value_is_valid && solution.value <= bracket_low.value |
| 431 | ? solution : bracket_low; |
| 432 | |
| 433 | summary->optimal_step_size = solution.x; |
| 434 | summary->success = true; |
| 435 | } |
| 436 | |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 437 | // Returns true if either: |
| 438 | // |
| 439 | // A termination condition satisfying the (strong) Wolfe bracketing conditions |
| 440 | // is found: |
| 441 | // |
| 442 | // - A valid point, defined as a bracket of zero width [zoom not required]. |
| 443 | // - A valid bracket (of width > tolerance), [zoom required]. |
| 444 | // |
| 445 | // Or, searching was stopped due to an 'artificial' constraint, i.e. not |
| 446 | // a condition imposed / required by the underlying algorithm, but instead an |
| 447 | // engineering / implementation consideration. But a step which exceeds the |
| 448 | // minimum step size, and satsifies the Armijo condition was still found, |
| 449 | // and should thus be used [zoom not required]. |
| 450 | // |
| 451 | // Returns false if no step size > minimum step size was found which |
| 452 | // satisfies at least the Armijo condition. |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 453 | bool WolfeLineSearch::BracketingPhase( |
| 454 | const FunctionSample& initial_position, |
| 455 | const double step_size_estimate, |
| 456 | FunctionSample* bracket_low, |
| 457 | FunctionSample* bracket_high, |
| 458 | bool* do_zoom_search, |
| 459 | Summary* summary) { |
| 460 | Function* function = options().function; |
| 461 | |
| 462 | FunctionSample previous = initial_position; |
| 463 | FunctionSample current = ValueAndGradientSample(step_size_estimate, 0.0, 0.0); |
| 464 | current.value_is_valid = false; |
| 465 | |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 466 | const double descent_direction_max_norm = |
| 467 | static_cast<const LineSearchFunction*>(function)->DirectionInfinityNorm(); |
| 468 | |
| 469 | *do_zoom_search = false; |
| 470 | *bracket_low = initial_position; |
| 471 | |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 472 | // As we require the gradient to evaluate the Wolfe condition, we always |
| 473 | // calculate it together with the value, irrespective of the interpolation |
| 474 | // type. As opposed to only calculating the gradient after the Armijo |
| 475 | // condition is satisifed, as the computational saving from this approach |
| 476 | // would be slight (perhaps even negative due to the extra call). Also, |
| 477 | // always calculating the value & gradient together protects against us |
| 478 | // reporting invalid solutions if the cost function returns slightly different |
| 479 | // function values when evaluated with / without gradients (due to numerical |
| 480 | // issues). |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 481 | ++summary->num_function_evaluations; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 482 | ++summary->num_gradient_evaluations; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 483 | current.value_is_valid = |
| 484 | function->Evaluate(current.x, |
| 485 | ¤t.value, |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 486 | ¤t.gradient); |
| 487 | current.gradient_is_valid = current.value_is_valid; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 488 | |
| 489 | while (true) { |
| 490 | ++summary->num_iterations; |
| 491 | |
| 492 | if (current.value_is_valid && |
| 493 | (current.value > (initial_position.value |
| 494 | + options().sufficient_decrease |
| 495 | * initial_position.gradient |
| 496 | * current.x) || |
| 497 | (previous.value_is_valid && current.value > previous.value))) { |
| 498 | // Bracket found: current step size violates Armijo sufficient decrease |
| 499 | // condition, or has stepped past an inflection point of f() relative to |
| 500 | // previous step size. |
| 501 | *do_zoom_search = true; |
| 502 | *bracket_low = previous; |
| 503 | *bracket_high = current; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 504 | VLOG(3) << std::scientific |
| 505 | << std::setprecision(kErrorMessageNumericPrecision) |
| 506 | << "Bracket found: current step (" << current.x |
| 507 | << ") violates Armijo sufficient condition, or has passed an " |
| 508 | << "inflection point of f() based on value."; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 509 | break; |
| 510 | } |
| 511 | |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 512 | if (current.value_is_valid && |
| 513 | fabs(current.gradient) <= |
| 514 | -options().sufficient_curvature_decrease * initial_position.gradient) { |
| 515 | // Current step size satisfies the strong Wolfe conditions, and is thus a |
| 516 | // valid termination point, therefore a Zoom not required. |
| 517 | *bracket_low = current; |
| 518 | *bracket_high = current; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 519 | VLOG(3) << std::scientific |
| 520 | << std::setprecision(kErrorMessageNumericPrecision) |
| 521 | << "Bracketing phase found step size: " << current.x |
| 522 | << ", satisfying strong Wolfe conditions, initial_position: " |
| 523 | << initial_position << ", current: " << current; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 524 | break; |
| 525 | |
| 526 | } else if (current.value_is_valid && current.gradient >= 0) { |
| 527 | // Bracket found: current step size has stepped past an inflection point |
| 528 | // of f(), but Armijo sufficient decrease is still satisfied and |
| 529 | // f(current) is our best minimum thus far. Remember step size |
| 530 | // monotonically increases, thus previous_step_size < current_step_size |
| 531 | // even though f(previous) > f(current). |
| 532 | *do_zoom_search = true; |
| 533 | // Note inverse ordering from first bracket case. |
| 534 | *bracket_low = current; |
| 535 | *bracket_high = previous; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 536 | VLOG(3) << "Bracket found: current step (" << current.x |
| 537 | << ") satisfies Armijo, but has gradient >= 0, thus have passed " |
| 538 | << "an inflection point of f()."; |
| 539 | break; |
| 540 | |
| 541 | } else if (current.value_is_valid && |
| 542 | fabs(current.x - previous.x) * descent_direction_max_norm |
| 543 | < options().min_step_size) { |
| 544 | // We have shrunk the search bracket to a width less than our tolerance, |
| 545 | // and still not found either a point satisfying the strong Wolfe |
| 546 | // conditions, or a valid bracket containing such a point. Stop searching |
| 547 | // and set bracket_low to the size size amongst all those tested which |
| 548 | // minimizes f() and satisfies the Armijo condition. |
| 549 | LOG_IF(WARNING, !options().is_silent) |
| 550 | << "Line search failed: Wolfe bracketing phase shrank " |
| 551 | << "bracket width: " << fabs(current.x - previous.x) |
| 552 | << ", to < tolerance: " << options().min_step_size |
| 553 | << ", with descent_direction_max_norm: " |
| 554 | << descent_direction_max_norm << ", and failed to find " |
| 555 | << "a point satisfying the strong Wolfe conditions or a " |
| 556 | << "bracketing containing such a point. Accepting " |
| 557 | << "point found satisfying Armijo condition only, to " |
| 558 | << "allow continuation."; |
| 559 | *bracket_low = current; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 560 | break; |
| 561 | |
| 562 | } else if (summary->num_iterations >= options().max_num_iterations) { |
| 563 | // Check num iterations bound here so that we always evaluate the |
| 564 | // max_num_iterations-th iteration against all conditions, and |
| 565 | // then perform no additional (unused) evaluations. |
| 566 | summary->error = |
| 567 | StringPrintf("Line search failed: Wolfe bracketing phase failed to " |
| 568 | "find a point satisfying strong Wolfe conditions, or a " |
| 569 | "bracket containing such a point within specified " |
| 570 | "max_num_iterations: %d", options().max_num_iterations); |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 571 | LOG_IF(WARNING, !options().is_silent) << summary->error; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 572 | // Ensure that bracket_low is always set to the step size amongst all |
| 573 | // those tested which minimizes f() and satisfies the Armijo condition |
| 574 | // when we terminate due to the 'artificial' max_num_iterations condition. |
| 575 | *bracket_low = |
| 576 | current.value_is_valid && current.value < bracket_low->value |
| 577 | ? current : *bracket_low; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 578 | break; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 579 | } |
| 580 | // Either: f(current) is invalid; or, f(current) is valid, but does not |
| 581 | // satisfy the strong Wolfe conditions itself, or the conditions for |
| 582 | // being a boundary of a bracket. |
| 583 | |
| 584 | // If f(current) is valid, (but meets no criteria) expand the search by |
| 585 | // increasing the step size. |
| 586 | const double max_step_size = |
| 587 | current.value_is_valid |
| 588 | ? (current.x * options().max_step_expansion) : current.x; |
| 589 | |
| 590 | // We are performing 2-point interpolation only here, but the API of |
| 591 | // InterpolatingPolynomialMinimizingStepSize() allows for up to |
| 592 | // 3-point interpolation, so pad call with a sample with an invalid |
| 593 | // value that will therefore be ignored. |
| 594 | const FunctionSample unused_previous; |
| 595 | DCHECK(!unused_previous.value_is_valid); |
| 596 | // Contracts step size if f(current) is not valid. |
| 597 | const double step_size = |
| 598 | this->InterpolatingPolynomialMinimizingStepSize( |
| 599 | options().interpolation_type, |
| 600 | previous, |
| 601 | unused_previous, |
| 602 | current, |
| 603 | previous.x, |
| 604 | max_step_size); |
| 605 | if (step_size * descent_direction_max_norm < options().min_step_size) { |
| 606 | summary->error = |
| 607 | StringPrintf("Line search failed: step_size too small: %.5e " |
| 608 | "with descent_direction_max_norm: %.5e", step_size, |
| 609 | descent_direction_max_norm); |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 610 | LOG_IF(WARNING, !options().is_silent) << summary->error; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 611 | return false; |
| 612 | } |
| 613 | |
| 614 | previous = current.value_is_valid ? current : previous; |
| 615 | current.x = step_size; |
| 616 | |
| 617 | ++summary->num_function_evaluations; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 618 | ++summary->num_gradient_evaluations; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 619 | current.value_is_valid = |
| 620 | function->Evaluate(current.x, |
| 621 | ¤t.value, |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 622 | ¤t.gradient); |
| 623 | current.gradient_is_valid = current.value_is_valid; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 624 | } |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 625 | |
| 626 | // Ensure that even if a valid bracket was found, we will only mark a zoom |
| 627 | // as required if the bracket's width is greater than our minimum tolerance. |
| 628 | if (*do_zoom_search && |
| 629 | fabs(bracket_high->x - bracket_low->x) * descent_direction_max_norm |
| 630 | < options().min_step_size) { |
| 631 | *do_zoom_search = false; |
| 632 | } |
| 633 | |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 634 | return true; |
| 635 | } |
| 636 | |
| 637 | // Returns true iff solution satisfies the strong Wolfe conditions. Otherwise, |
| 638 | // on return false, if we stopped searching due to the 'artificial' condition of |
| 639 | // reaching max_num_iterations, solution is the step size amongst all those |
| 640 | // tested, which satisfied the Armijo decrease condition and minimized f(). |
| 641 | bool WolfeLineSearch::ZoomPhase(const FunctionSample& initial_position, |
| 642 | FunctionSample bracket_low, |
| 643 | FunctionSample bracket_high, |
| 644 | FunctionSample* solution, |
| 645 | Summary* summary) { |
| 646 | Function* function = options().function; |
| 647 | |
| 648 | CHECK(bracket_low.value_is_valid && bracket_low.gradient_is_valid) |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 649 | << std::scientific << std::setprecision(kErrorMessageNumericPrecision) |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 650 | << "Ceres bug: f_low input to Wolfe Zoom invalid, please contact " |
| 651 | << "the developers!, initial_position: " << initial_position |
| 652 | << ", bracket_low: " << bracket_low |
| 653 | << ", bracket_high: "<< bracket_high; |
| 654 | // We do not require bracket_high.gradient_is_valid as the gradient condition |
| 655 | // for a valid bracket is only dependent upon bracket_low.gradient, and |
| 656 | // in order to minimize jacobian evaluations, bracket_high.gradient may |
| 657 | // not have been calculated (if bracket_high.value does not satisfy the |
| 658 | // Armijo sufficient decrease condition and interpolation method does not |
| 659 | // require it). |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 660 | // |
| 661 | // We also do not require that: bracket_low.value < bracket_high.value, |
| 662 | // although this is typical. This is to deal with the case when |
| 663 | // bracket_low = initial_position, bracket_high is the first sample, |
| 664 | // and bracket_high does not satisfy the Armijo condition, but still has |
| 665 | // bracket_high.value < initial_position.value. |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 666 | CHECK(bracket_high.value_is_valid) |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 667 | << std::scientific << std::setprecision(kErrorMessageNumericPrecision) |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 668 | << "Ceres bug: f_high input to Wolfe Zoom invalid, please " |
| 669 | << "contact the developers!, initial_position: " << initial_position |
| 670 | << ", bracket_low: " << bracket_low |
| 671 | << ", bracket_high: "<< bracket_high; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 672 | |
| 673 | if (bracket_low.gradient * (bracket_high.x - bracket_low.x) >= 0) { |
| 674 | // The third condition for a valid initial bracket: |
| 675 | // |
| 676 | // 3. bracket_high is chosen after bracket_low, s.t. |
| 677 | // bracket_low.gradient * (bracket_high.x - bracket_low.x) < 0. |
| 678 | // |
| 679 | // is not satisfied. As this can happen when the users' cost function |
| 680 | // returns inconsistent gradient values relative to the function values, |
| 681 | // we do not CHECK_LT(), but we do stop processing and return an invalid |
| 682 | // value. |
| 683 | summary->error = |
| 684 | StringPrintf("Line search failed: Wolfe zoom phase passed a bracket " |
| 685 | "which does not satisfy: bracket_low.gradient * " |
| 686 | "(bracket_high.x - bracket_low.x) < 0 [%.8e !< 0] " |
| 687 | "with initial_position: %s, bracket_low: %s, bracket_high:" |
| 688 | " %s, the most likely cause of which is the cost function " |
| 689 | "returning inconsistent gradient & function values.", |
| 690 | bracket_low.gradient * (bracket_high.x - bracket_low.x), |
| 691 | initial_position.ToDebugString().c_str(), |
| 692 | bracket_low.ToDebugString().c_str(), |
| 693 | bracket_high.ToDebugString().c_str()); |
| 694 | LOG_IF(WARNING, !options().is_silent) << summary->error; |
| 695 | solution->value_is_valid = false; |
| 696 | return false; |
| 697 | } |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 698 | |
| 699 | const int num_bracketing_iterations = summary->num_iterations; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 700 | const double descent_direction_max_norm = |
| 701 | static_cast<const LineSearchFunction*>(function)->DirectionInfinityNorm(); |
| 702 | |
| 703 | while (true) { |
| 704 | // Set solution to bracket_low, as it is our best step size (smallest f()) |
| 705 | // found thus far and satisfies the Armijo condition, even though it does |
| 706 | // not satisfy the Wolfe condition. |
| 707 | *solution = bracket_low; |
| 708 | if (summary->num_iterations >= options().max_num_iterations) { |
| 709 | summary->error = |
| 710 | StringPrintf("Line search failed: Wolfe zoom phase failed to " |
| 711 | "find a point satisfying strong Wolfe conditions " |
| 712 | "within specified max_num_iterations: %d, " |
| 713 | "(num iterations taken for bracketing: %d).", |
| 714 | options().max_num_iterations, num_bracketing_iterations); |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 715 | LOG_IF(WARNING, !options().is_silent) << summary->error; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 716 | return false; |
| 717 | } |
| 718 | if (fabs(bracket_high.x - bracket_low.x) * descent_direction_max_norm |
| 719 | < options().min_step_size) { |
| 720 | // Bracket width has been reduced below tolerance, and no point satisfying |
| 721 | // the strong Wolfe conditions has been found. |
| 722 | summary->error = |
| 723 | StringPrintf("Line search failed: Wolfe zoom bracket width: %.5e " |
| 724 | "too small with descent_direction_max_norm: %.5e.", |
| 725 | fabs(bracket_high.x - bracket_low.x), |
| 726 | descent_direction_max_norm); |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 727 | LOG_IF(WARNING, !options().is_silent) << summary->error; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 728 | return false; |
| 729 | } |
| 730 | |
| 731 | ++summary->num_iterations; |
| 732 | // Polynomial interpolation requires inputs ordered according to step size, |
| 733 | // not f(step size). |
| 734 | const FunctionSample& lower_bound_step = |
| 735 | bracket_low.x < bracket_high.x ? bracket_low : bracket_high; |
| 736 | const FunctionSample& upper_bound_step = |
| 737 | bracket_low.x < bracket_high.x ? bracket_high : bracket_low; |
| 738 | // We are performing 2-point interpolation only here, but the API of |
| 739 | // InterpolatingPolynomialMinimizingStepSize() allows for up to |
| 740 | // 3-point interpolation, so pad call with a sample with an invalid |
| 741 | // value that will therefore be ignored. |
| 742 | const FunctionSample unused_previous; |
| 743 | DCHECK(!unused_previous.value_is_valid); |
| 744 | solution->x = |
| 745 | this->InterpolatingPolynomialMinimizingStepSize( |
| 746 | options().interpolation_type, |
| 747 | lower_bound_step, |
| 748 | unused_previous, |
| 749 | upper_bound_step, |
| 750 | lower_bound_step.x, |
| 751 | upper_bound_step.x); |
| 752 | // No check on magnitude of step size being too small here as it is |
| 753 | // lower-bounded by the initial bracket start point, which was valid. |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 754 | // |
| 755 | // As we require the gradient to evaluate the Wolfe condition, we always |
| 756 | // calculate it together with the value, irrespective of the interpolation |
| 757 | // type. As opposed to only calculating the gradient after the Armijo |
| 758 | // condition is satisifed, as the computational saving from this approach |
| 759 | // would be slight (perhaps even negative due to the extra call). Also, |
| 760 | // always calculating the value & gradient together protects against us |
| 761 | // reporting invalid solutions if the cost function returns slightly |
| 762 | // different function values when evaluated with / without gradients (due |
| 763 | // to numerical issues). |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 764 | ++summary->num_function_evaluations; |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 765 | ++summary->num_gradient_evaluations; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 766 | solution->value_is_valid = |
| 767 | function->Evaluate(solution->x, |
| 768 | &solution->value, |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 769 | &solution->gradient); |
| 770 | solution->gradient_is_valid = solution->value_is_valid; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 771 | if (!solution->value_is_valid) { |
| 772 | summary->error = |
| 773 | StringPrintf("Line search failed: Wolfe Zoom phase found " |
| 774 | "step_size: %.5e, for which function is invalid, " |
| 775 | "between low_step: %.5e and high_step: %.5e " |
| 776 | "at which function is valid.", |
| 777 | solution->x, bracket_low.x, bracket_high.x); |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 778 | LOG_IF(WARNING, !options().is_silent) << summary->error; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 779 | return false; |
| 780 | } |
| 781 | |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 782 | VLOG(3) << "Zoom iteration: " |
| 783 | << summary->num_iterations - num_bracketing_iterations |
| 784 | << ", bracket_low: " << bracket_low |
| 785 | << ", bracket_high: " << bracket_high |
| 786 | << ", minimizing solution: " << *solution; |
| 787 | |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 788 | if ((solution->value > (initial_position.value |
| 789 | + options().sufficient_decrease |
| 790 | * initial_position.gradient |
| 791 | * solution->x)) || |
| 792 | (solution->value >= bracket_low.value)) { |
| 793 | // Armijo sufficient decrease not satisfied, or not better |
| 794 | // than current lowest sample, use as new upper bound. |
| 795 | bracket_high = *solution; |
| 796 | continue; |
| 797 | } |
| 798 | |
| 799 | // Armijo sufficient decrease satisfied, check strong Wolfe condition. |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 800 | if (fabs(solution->gradient) <= |
| 801 | -options().sufficient_curvature_decrease * initial_position.gradient) { |
| 802 | // Found a valid termination point satisfying strong Wolfe conditions. |
Carlos Hernandez | 79397c2 | 2014-08-07 17:51:38 -0700 | [diff] [blame] | 803 | VLOG(3) << std::scientific |
| 804 | << std::setprecision(kErrorMessageNumericPrecision) |
| 805 | << "Zoom phase found step size: " << solution->x |
| 806 | << ", satisfying strong Wolfe conditions."; |
Sascha Haeberling | 1d2624a | 2013-07-23 19:00:21 -0700 | [diff] [blame] | 807 | break; |
| 808 | |
| 809 | } else if (solution->gradient * (bracket_high.x - bracket_low.x) >= 0) { |
| 810 | bracket_high = bracket_low; |
| 811 | } |
| 812 | |
| 813 | bracket_low = *solution; |
| 814 | } |
| 815 | // Solution contains a valid point which satisfies the strong Wolfe |
| 816 | // conditions. |
| 817 | return true; |
| 818 | } |
| 819 | |
| 820 | } // namespace internal |
| 821 | } // namespace ceres |